Stability of differential-difference systems with indefinite parameters (Q864387)

Consider the system of linear delay differential equations \[ \frac{dx (t)}{dt}= A_1x(t)+A_2x(t-h),\tag{*} \] where \(A_1\) and \(A_2\) are \(n \times n\)-matrices. The authors assume that system (*) is asymptotically stable for \(h=0\). They estimate the maximal delay such that system (*) is asymptotically stable and the roots of the corresponding characteristic equation satisfy some additional conditions.